I live a block from the Back Bay Logan Express pickup (yes, the Back Bay service shares the name as the Logan Express that goes out in the suburbs to Peabody/Framingham/Woburn/Braintree, which is not at all confusing) by the Pru and take it a fair amount — would say going to Logan it's somewhat timely (supposed to leave Back Bay on the half hour, but it typically runs 5 - 10 minutes late), while from Logan it's kind of a crapshoot. The Transit app (https://transitapp.com/region/boston) shows real-time bus locations, which can be helpful for timing / predicting things as well.

In terms of traffic — I avoid the LEX (and the Silver Line, which also isn't great for Back Bay anyway) during peak hours since they both take I-90/the Ted Williams tunnel to Logan and prefer the Green Line -> Blue Line route, but off-peak it's fine (check Google Maps to see how slow I-90 is). Also thanks to the quirks of the Mass Pike when going inbound to Logan you'll first backtrack to the Allston/Brighton exit before turning around, and the same thing coming into the city (so don't be confused when you think the bus is going the "wrong" direction).

You can buy tickets from the website very easily (and it's free from Logan inbound, so no need to buy a round trip) — it takes maybe 2 minutes (typing in your credit card number is the slowest step) and you just show the QR code to the bus operator when you board; I typically purchase mine as I'm walking down Boylston to the pickup point (or while waiting for the bus itself).